When my posts have no images, they are shared in Facebook with icon.
At first the facebook icon had been shown.
When I added a Delicious account, new posts started to be shown in facebook with the Delicious icon.

Is it possible not to show any icons in Facebook when there are no images in post? Maybe this icons are set as some default image?

Plugin takes featured image from the post. if there is no featured image it will take the first image from the post body. if your post body has no images it will take the specified default image. if default image is not specified it will take first image from the page.

Please set featured image to clearly define what image you would like to show or specify Plugin Settings->Other Settings->"Open Graph" Tags->Default Image URL for og:image tag for the default image.